论文标题
Gottlieb元素对空间的Sullivan最小模型的结构效果
The structuring effect of a Gottlieb element on the Sullivan minimal model of a space
论文作者
论文摘要
我们在简单连接的空间$ x $的合理同喻中显示了Gottlieb元素，这意味着Sullivan最小模型的结构性结果，其结果取决于奇偶校验。在均匀的情况下，我们证明了一个有理的Gottlieb元素是终端均匀元素。这一事实使我们能够完成杜邦的论点，以证明均匀的Gottlieb元素为有限类型的正式空间的合理共同体提供了自由因素。我们将奇数结果应用于有限综合体的Gottlieb元素上的$ 2N $转换的特殊情况。我们将结果结合在一起，为分类空间的实现问题做出贡献，$ b \ mathrm {aut} _1（x）$。 We prove a simply connected space $X$ satisfying $B\mathrm{aut}_1(X_{\mathbb{Q}}) \simeq S_{\mathbb{Q}}^{2n}$ must have infinite-dimensional rational homotopy and vanishing rational Gottlieb elements above degree $2n-1$ for $n= 1, 2，3。$
We show a Gottlieb element in the rational homotopy of a simply connected space $X$ implies a structural result for the Sullivan minimal model, with different results depending on parity. In the even-degree case, we prove a rational Gottlieb element is a terminal homotopy element. This fact allows us to complete an argument of Dupont to prove an even-degree Gottlieb element gives a free factor in the rational cohomology of a formal space of finite type. We apply the odd-degree result to affirm a special case of the $2N$-conjecture on Gottlieb elements of a finite complex. We combine our results to make a contribution to the realization problem for the classifying space $B\mathrm{aut}_1(X)$. We prove a simply connected space $X$ satisfying $B\mathrm{aut}_1(X_{\mathbb{Q}}) \simeq S_{\mathbb{Q}}^{2n}$ must have infinite-dimensional rational homotopy and vanishing rational Gottlieb elements above degree $2n-1$ for $n= 1, 2, 3.$
